spectroscopic ellipsometry and reflectometry from gratings...

Fred L. Terry, Jr., ICSE-3, Vienna, Austria, July 7, 20031

Spectroscopic Ellipsometry and Reflectometry from Gratings (Scatterometry) for Critical Dimension Measurement and in

situ, Real-Time Process Monitoring

Fred L. Terry, Jr.

Dept of EECS / University of Michigan+1-734-763-9764

+1- 734-763-9324 (fax)[email protected]

http://www.eecs.umich.edu/~fredty


Outline

• Goals, Background, Theory• Ex Situ Measurements for Topography

Extraction• In Situ Movies of Topography Evolution in

Reactive Ion Etcher• Limitations• Conclusions, Challenges, Future Work


Goals & Background• Nondestructive, High Speed Extraction of

Information from Patterned Structures– Critical Dimensions– Wall Shapes– Film Thicknesses

• Ideally Also Usable in situ for Real-Time Monitoring and Control of Fabrication Processes

• Exciting Work Present by H. Maynard at ICSE-2– Limited Applicability Due to Diffraction Effects

⇒ Use Structures for which the Diffraction Problem Can Be Accurately Solved


Background I

• Basic Concept: Scattering (Diffraction) of Light from Features Produces Strong Structure in Reflected Optical Field

• Analyze Unique Data to Obtain Topography Information

• Periodic Structures (Gratings) Can Be Numerically Modeled “Exactly”

• Feature Resolutions Much Better than Rayleigh Limit Are Possible Since This Is Not A General Image Formation Problem

– Periodicity of Structure Is Known– Dielectric Functions of Materials Are Known


Background IISingle Wavelength Scatterometry• Examine Structure in Specular and/or Diffracted

Modes vs. Angle of Incidence at a Single Wavelength– Naqvi, McNeil, and Co-workers (UNM)– Elta, Terry, and Co-workers (U. Michigan)– Texas Instruments, Sandia Systems⇒Biorad ⇒Accent

Spectroscopic Ellipsometry and Reflectometry• Examine Structure vs. Wavelength at Fixed AOI

– Terry and Co-workers (U. Michigan)– Spanos and Co-workers (UCB) ⇒ Timbre Technologies– IBM ⇒ Nanometrics– KLA-Tencor, ThermaWave/Sensys, Nova


Spectroscopic Ellipsometry

• Tan(Ψ) And Cos(∆) Are Measured by Ellipsometry—Functions of wavelength and incident angle

)cos()2sin( ),2cos(

)exp()tan(//

∆⋅Ψ=Ψ=

∆⋅Ψ===

βα

ρ iEEEE

RR

isrs

iprp

s

p

Substrate

Thin Film Stack

Eip

Eis

Erp

Ers

Light Source

Polarizer Analyzer

Monochromator&

Detector

Sample with Grating


Rigorous Coupled-Wave Analysis Method of Moharam and Gaylord

• The Line is Sliced into a Number of Thin Layers• Numerical Eigen-Matrix Solution for Maxwell’s Equations• Amplitudes & Phases of Different Diffraction Orders Are

Obtained by Matching the EM Boundary Conditions

2ε-1 1

2-2Transmitted Waves

0

1-1Reflected Waves

t

dθ

1ε


RCWA Computation Issues• Let N be the number of spatial harmonics retained for

approximating the solution,• s be the number of slices used for approximating grating profile,• Then at each wavelength we need

– 4Ns linear equations for p-polarization– 2(N+1)s linear equations for s-polarization

• Number of Required Slices (s) Depends on Shape of Line (typical 10-30)

• Number of Require Spatial Harmonics Depends on Λ/λ, ε of materials (typical 15-100)

• Large Scale Computation but Vectorizes Naturally for Parallel Processing (each λ independent)

• Continuing Advances by Computational E&M Theory Community


Grating ⇔ Anisotropic Thin Film Analogy

Λ

ε1(λ)

ε2(λ) ε2(λ) ε2(λ)

ε1(λ) ε1(λ) ε1(λ)

W

D

Substrate

Thin Film Stack

( )ε λ

Substrate

Thin Film Stack

D εx

εz

εy

1-D Grating Anisotropic Thin Film

• Line Height ⇔ Film Thickness

• Line Shape ⇔ Optical Dielectric Function


Specular Spectroscopic Scatterometry• Probes Wavelength Dependence of Scattering from a

Given Line Size/Shape• Grating Amplifies & Averages Single Line Effects• Grating Periodicity Aids Accurate Diffraction Solution• Result Sub-Wavelength Topography Sensitivity• Extremely High Sensitivity to Line Height (D) ⇒

Analogous to Thin Film Thickness• Very Good Sensitivity to Linewidth (W) & Line-shape

Under Proper Circumstances ⇒ Analogous to Parameterized Extraction of Optical Dielectric Function of Thin Film

• Accuracy of Topography Extraction Analogous to Accuracy of ε(λ) Extraction From Thin Films Using SE

– Will Fail If Grating Is Too Shallow (Effective Optical Thickness Fails to Produce Thin Film Interference Effect)


Topography Extraction Example W>λmin

• Experimental Data Taken at 7° AOI with Sopra GESP-5 Ellipsometer

• 350 nm Line/ 700 nm Period Grating Etched in Single Crystal Si

• 350 nm Line/ 700 nm Period Photoresist on 31.7nm SiO2 on Si

• Successively Improved Topography Estimations Using Levenberg-Marquardt Non-Linear Regression

– Trapezoid (3 parameters)– Trapezoid on Rectangular Base (4 parameters)– Triangular Top on Trapezoid on Rectangle (5 parameters)– 3 Quadratic Segments with Zero Top Width (Triangle-Trapezoid-

Trapezoid with Curvature, 9 parameters)


Etch Experiment Description• Lam TCP9400SE Plasma Etching System• Cl2/HBr Si Main Etch Recipe• Nominal Etching Rates:

– Oxide 5.43Å/sec– Poly 52.1Å/sec

• Times: 60, 77, 97, 116, 135, 154, 174 sec


Near Normal SE for RIE Etched Si Grating

SE & RCWA

SEM

CD (nm)

323±1.6

323±5

Depth (µm)

331±0.4

340±5

Wall Angle

83.2° ±0.29°

84.1° ±1.4°

-1

-0.5

0

0.5

1

0.3 0.4 0.5 0.6 0.7 0.8

alpha measuredalpha fitbeta measuredbeta fit

alph

a, b

eta

wavelength (µm)

Angle of Incidence=7 Degrees


Time Evolved SE Data and FittingIncidence at 7°

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

0.4 0.6 0.8-1

0

1

β

α

λ (µm)

λ (µm)

• : Experiment— : Theory

Etching Time


Submicron Grating• ~0.35µm Line/Space

Grating In Photoresist/300Å SiO2/Si

• Accurate Photoresist N(λ) Obtained by SE Measurement of Similarly Prepared Unpatterned Film

• Period Measured as 0.700 µm Using 1st Order Diffraction Angle at Multiple λ’s


Trapezoidal Fit 400-825 nm


Trapezoidal Fit


Trapezoid on Rectangle Fit


Triangle-Trapezoid-Rectangle Fit


3-Segment Quadratic Fit


Extracted Topography Comparison


3-Level Quadratic Fit Parameters, Confidence

Limits, & Cross-

Correlation Coefficients

Term Value 95.4% conf. Limit Units

h1 146.51 4.55 nm m11 0.7389 0.0097 slope m12 -0.4698 0.011 quadratic curvature



h1 m11 m12 h2 m21 m22 h3 m31 m32 h1 1 0.356-0.217-0.369-0.176 0.121 0.267 0.101 0.04m11 0.356 1 -0.88 -0.34 -0.31 0.354 0.301-0.098 0.219m12-0.217 -0.88 1 0.373 -0.02 -0.08-0.363-0.146-0.009h2 -0.369 -0.34 0.373 1 0.512 -0.527-0.993-0.369-0.108m21-0.176 -0.31 -0.02 0.512 1 -0.981-0.493 0.286-0.474m22 0.121 0.354 -0.08-0.527-0.981 1 0.517 -0.31 0.501h3 0.267 0.301-0.363-0.993-0.493 0.517 1 0.394 0.082m31 0.101-0.098-0.146-0.369 0.286 -0.31 0.394 1-0.866m32 0.04 0.219-0.009-0.108-0.474 0.501 0.082-0.866 1

Fit Was Pushed to the Limits of Data


In Situ Measurements: Real-Time Monitoring and Control

Movies


LAM TCP 9400 SE with SOPRA RTSE

Thanks to Dr. Helen Maynard, Lucent Bell Labs for Assistance with Port Layout


Real-Time Ellipsometry Pararmeters

• 63.5° AOI Dictated by Geometry of Etch System• RTSE System Run at Maximum Data Collection

Rates Due to Fast Time Scale of Industrial Etch Processes (~100 s total times, Etch Rates ~3-5 nm/s)

• Single-Turn of Polarizer Data Sampling Time (0.1 s)– Capture Data with Only few 0.1’s nm Thickness Change During

Samplin• Minimum Data Acquistion Time ~1 sample/0.18s • Usable Data for λ=300-780 nm• Fixed Analyzer Angle 45°


Example Process Critical Dimension Control: Etch to Target

Gate Poly

Si Substrate

Gate Oxide SiO2

Hard Mask SiO2

PR

CD

PR

CD

PR

CD

Reactive Ion Etch to Shrink CD to a Desired DimensionGoal: Achieving Same Final CD regardless of Incoming

CD & RIE Process Variation


Experiment Description~350nm Line/Space

Grating• Lam 9400 TCP Etcher• O2 Plasma Gas• Target: Trim Bottom CD to

200nm• Non-Linear Filter Method to

Detect Endpoint and Shut-Off Plasma

• This Experiment Stopped at 200nm

• Work of Drs. Hsu-Ting Huang, Ji-Woong Lee, Pramod Khargonekar, and Fred Terry


In Situ Optical CD/Automated Etch to Target CD

• O2 Plasma Photoresist Trim in Lam 9400 TCP

• In Situ Real-Time Spectroscopic Ellipsometry Monitoring of Photoresist Grating Structure

• Off-Line RCWA Analysis of Grating Diffraction Problem

• Nonlinear Filtering Algorithm for Real-Time Data Analysis

– Completely Hands-off Automated Etch to Target CD

• Before Etching (top):– Bottom CD: 296 nm– Feature Height: 777 nm

• After Trim-back (bottom):– Bottom CD: 200 nm (target)– Feature Height: 697 nm

Trimmed:CD 189.1±29.3nm

Height 710.9 ±67.6nm

Start:CD 296.7±9.1nm

Height 790.0 ±63.4nm


Experimental Description• Lam TCP9400SE Plasma Etching System• Plasma Gas: HBr 100 sccm & Cl2 15 sccm• Nominal Etching Rate: PR 5Å/sec, Oxide 3.6Å/sec, and Poly 30Å/sec

PR

CD

PR

CD

PR

CDSiO2 SiO2 SiO2

Si Substrate


Comparison of PR-Masked Si Etch to SEM Cross-Section

• Si Trench Depth 173.32 ± 0.26 nm• Si CD 354.62 ± 11.37 nm


Limitations & Challenges


RTSE Etch Monitoring: Over-Fitting

• Attempt to Fit for Under-Cut of Resist• Over-Parameterization Due to Limited

Absolute Accuracy of Measurement• In This Case, Accuracy is Limited by Stray

Light, Lower UV Photon Counts– Usable Minimum Wavelength ~300nm– Some Distortion of Peak/Valley Shapes


Cruelty of Diffraction Physics:W/λmin + εline Control Strength of Scattering

W λmin /2 to λmin High Sensitivity to Detailed Shape in Structure of Data vs. λ

W≈λmin /10 to λmin/2 Sensitivity to Average CD, Diminishing Shape Information

Most Shape Info in Magnitude not Fine Structure of Data

W

vs.

fixed

λminW λmin Results Converge to EMA, No Real CD Info, Only Average Composition


Simulations of ITRS Photoresist Milestones

• Simulated Data using Model DUV Photoresist at 2010, 2013, and 2016 Technology Nodes

• Rectangular Profiles Assumed with:– Λ=90nm W=25±1.5nm Thick=100nm– Λ=64nm W=18 ± 1.1nm Thick=80nm– Λ=44nm W=13 ± 0.7nm Thick=50nm

• Assumed 190-800nm Spectroscopic Ellipsometry Measurements

• Good News: Diminishing but Usable CD Sensitivity to 2016

• Bad News: Loss of Detailed Shape Sensitivity even at 2010


Simulated ~40nm PR Line Λ=90nm

200 300 400 500 600 700 800-1

-0.5

0

0.5

1Alpha

wavelength (nm)

Alp

ha

200 300 400 500 600 700 800-1

-0.5

0

0.5

1Beta

wavelength (nm)

Bet

a

-60 -40 -20 0 20 40 600

20

40

60

80

100

120

nm

nm

Can Detailed Shape Information Be Extracted?


Fit Using Rectangular Only Model

200 300 400 500 600 700 800-1

-0.5

0

0.5

1Alpha

wavelength (nm)

Alp

ha

200 300 400 500 600 700 800-5

0

5

wavelength (nm)

Cha

nge

in A

lpha

x 1

00

200 300 400 500 600 700 800-1

-0.5

0

0.5

1Beta

wavelength (nm)

Bet

a

200 300 400 500 600 700 800-4

-2

0

2

wavelength (nm)

Cha

nge

in B

eta

x 10

0

-60 -40 -20 0 20 40 600

20

40

60

80

100

120 • Rectangle Fit Averages More Complex Structure

• Examine Structure Differences in Data Through Derivatives vs. λ


d3β/dλ3 For Complex Line & Rectangular Fit

-60 -40 -20 0 20 40 600

20

40

60

80

100

120

200 300 400 500 600 700 800-8

-6

-4

-2

0

2

4

6x 10-4

nm

d3 β/dλ

3

No Structural Difference in Data Vs. Fit, All Information Concerning the More Complex Shape is in the Small Absolute Differences


Structure of Data and Fit• Fitting with a Rectangle-Only Geometry Yields NO

Structure Differences, Only Magnitude Differences• Examining Derivatives of Data and Fit Illustrates

Complete Lack of Structural Differences• VERY High Instrument Accuracy Needed For

Detailed Topography Extraction Without Resorting to VUV Measurements

• High Accuracy RCWA Calculations Required for Simulation/Regression

• VUV & EUV Scatterometry Needed for the Future


Conclusions & Challenges

• Spectroscopic Ellipsometry + Accurate Diffraction Modeling Allows Topography Extraction with Resolution λ

• in situ Applications Allow Fabrication Processes to be Studied and Controlled in New Ways

• Wide-Spread Deployment in IC Industry• 2-D Arrays Under Development by Several

Companies• Exploratory Line-Edge Roughness Extraction

Work Underway


Conclusions & Challenges

• Diffraction Modeling for Non-Periodic Structures

– Process Control on Real Product IC’s– Applications in Biology and other “Messy” Fields

• Instrumentation and Measurement Schemes for Isolated or Sparse Structures

• Detailed Understanding of Accuracy Limitations, Parameter Correlation Effects, etc.


Acknowledgements• Collabators:

– Drs. Hsu-Ting Huang, Pete Klimecky, Wei Kong, Ji_Woong Lee, Meng-En Lee, Brooke Stutzman

– Prof. Pramod Khargonekar– Dr. Dennis Grimard, Mr. Dennis Swieger, and Mr. Jeff Fournier

• Initial Work Funded by SRC Center of Excellence for Automated Semiconductor Manufacturing

– Project Ended August, 1999

• Research funded in part by: AFOSR/DARPA MURI Center for Intelligent Electronics Manufacturing (AFOSR F49620-95-1-0524)

– Projected Ended August, 2001

• Research funded in part by: NIST Intelligent Control of the Semiconductor Patterning Process (70NANB8H4067)

– Project Ended June, 2002

spectroscopic ellipsometry and reflectometry from gratings...

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